How do I generate a tone in only one channel? And how do I generate separate tones in each channel?

When you generate your original tone, make sure it's a stereo tone you create. Any subsequent tone should be mono. Now, using the channel controls:

... you can mute one of them - I've muted the RH channel. This means that any operations you carry out will only happen to the 'live' channel (mute button is ringed in red). So if you copy the second (mono) tone to that channel, it will leave the original alone, and you'll have the second tone on the other channel, so you'll hear both of them when you un-mute. If you just want the other channel silent, it's even easier - mute the one you want to keep, select Effects>Silence and it will knock out the other one completely.